Under pressure from activist Elliott Associates, Hess is slimming down and plans to repurchase shares. Why Elliott thinks the energy company could be worth $126 a share.

Hess, a global energy producer, is undergoing a makeover that could leave it a slimmer but stronger oil-patch gem.

The New York-based company, under pressure from activist investor Elliott Management, has been working to shed assets, including its oil-storage terminals, energy-trading and market operations, and several international properties, in order to focus on exploration and production. The company also plans to unload 1,350...